Background

This analysis document compliments FIA - NLS Models: Biomass Growth vs. Stand Age. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different growth estimators.

Here, we fit the models using: 1) calculated plot biomass growth (Mass-Balance method) using only trees >5 inches (12.5 cm) dbh (\(G_{MassBal > 5}\)), and 2) plot biomass growth (tree incremental growth method) for trees >5 inches (12.5 cm) dbh (\(G_{TI-NoIngrow}\)).

Below the model fitting procedure is implemented by ecoprovince:

Analysis 1: \(G_{MassBal > 5}\)

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6869     3003.0                                
## 2   6817     2319.6 52 683.36  38.621 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29089.03
## 2     2 27204.41
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.38487    0.27356   5.062 4.25e-07 ***
## alpha  0.18115    0.03979   4.553 5.39e-06 ***
## a      0.52635    0.16513   3.187  0.00144 ** 
## b      2.18400    0.19076  11.449  < 2e-16 ***
## c     52.12308    0.96256  54.151  < 2e-16 ***
## d      1.31622    0.08559  15.379  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5833 on 6817 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (54 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  19351    10991.7                                 
## 2  18862     6848.8 489 4142.9  23.333 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 82798.28
## 2     2 72717.04
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.04368    0.24809   8.238  < 2e-16 ***
## alpha  0.18402    0.02816   6.535 6.53e-11 ***
## a      0.33754    0.02113  15.978  < 2e-16 ***
## b      1.67224    0.06022  27.767  < 2e-16 ***
## c     41.35770    0.42247  97.894  < 2e-16 ***
## d      1.23219    0.02206  55.859  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6026 on 18862 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3847 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 45 rows containing missing values (`geom_point()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7319     3321.1                                
## 2   7255     2929.5 64  391.6  15.153 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33832.56
## 2     2 32731.56
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.60471    0.14205  -4.257 2.10e-05 ***
## alpha  0.54725    0.04161  13.152  < 2e-16 ***
## a      1.24080    0.45261   2.741  0.00613 ** 
## b      3.34106    0.46029   7.259 4.32e-13 ***
## c     46.44359    1.92195  24.165  < 2e-16 ***
## d      1.75442    0.20430   8.588  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6354 on 7255 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (72 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 6 rows containing missing values (`geom_point()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   5044     2546.6                                 
## 2   4824     1164.1 220 1382.5   26.04 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25129.16
## 2     2 20639.78
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.27611    0.26038   1.060    0.289    
## alpha  0.40648    0.05148   7.896 3.54e-15 ***
## a      0.75525    0.11162   6.766 1.48e-11 ***
## b      2.61616    0.16019  16.332  < 2e-16 ***
## c     52.52465    1.61457  32.532  < 2e-16 ***
## d      1.34330    0.07403  18.147  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4912 on 4824 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1015 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   8872     3730.1                                 
## 2   8730     2486.8 142 1243.2  30.736 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40473.24
## 2     2 36461.41
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.46732    0.13024  -3.588 0.000335 ***
## alpha  0.37517    0.04337   8.651  < 2e-16 ***
## a      1.27585    0.34147   3.736 0.000188 ***
## b      2.57339    0.34328   7.497 7.19e-14 ***
## c     36.25752    1.19232  30.409  < 2e-16 ***
## d      1.48024    0.16001   9.251  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5337 on 8730 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1274 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 6 rows containing missing values (`geom_point()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13446     8033.9                                 
## 2  13195     6851.0 251 1182.9  9.0765 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69488.49
## 2     2 66713.48
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.25713    0.23997   9.406  < 2e-16 ***
## alpha  0.60282    0.02224  27.100  < 2e-16 ***
## a      0.66299    0.08902   7.448 1.01e-13 ***
## b      3.47069    0.14354  24.180  < 2e-16 ***
## c     24.60260    0.33688  73.030  < 2e-16 ***
## d      1.53924    0.04462  34.494  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7206 on 13195 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (316 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 30 rows containing missing values (`geom_point()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13504     9840.7                                 
## 2  13221     9032.3 283  808.4  4.1812 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69847.07
## 2     2 67892.53
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.82450    0.24314   7.504 6.58e-14 ***
## alpha  0.58974    0.02275  25.921  < 2e-16 ***
## a      0.52603    0.11031   4.769 1.87e-06 ***
## b      3.39759    0.16067  21.146  < 2e-16 ***
## c     23.73576    0.38312  61.954  < 2e-16 ***
## d      1.62726    0.05587  29.128  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8265 on 13221 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (402 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 66 rows containing missing values (`geom_point()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1368    1225.98                                
## 2   1316     933.16 52 292.82  7.9413 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7586.402
## 2     2 7029.295
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.64588    1.04477   1.575   0.1154    
## alpha  0.71337    0.09113   7.828 1.02e-14 ***
## a      1.72798    1.57006   1.101   0.2713    
## b      2.11173    1.58240   1.335   0.1823    
## c     26.02966    3.65593   7.120 1.77e-12 ***
## d      1.54134    0.92973   1.658   0.0976 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8421 on 1316 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89837, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.0397, p-value = 4.663e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 5 rows containing missing values (`geom_point()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1888     947.45                                 
## 2   1773     380.66 115 566.79  22.956 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9343.582
## 2     2 7300.531
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.06042    0.55389   1.914  0.05572 .  
## alpha  0.05979    0.10882   0.549  0.58278    
## a      1.57196    0.35126   4.475 8.12e-06 ***
## b      0.95517    0.34402   2.776  0.00555 ** 
## c     40.21823    3.57484  11.250  < 2e-16 ***
## d      1.22899    0.37861   3.246  0.00119 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4634 on 1773 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (516 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.81074, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.9337, p-value = 4.099e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    710    1183.68                                
## 2    667     955.57 43  228.1  3.7028 2.639e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3587.653
## 2     2 3324.689
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.5528     1.8132   0.856  0.39210    
## alpha   0.4145     0.1902   2.179  0.02971 *  
## a       0.8692     0.3061   2.840  0.00466 ** 
## b       1.8594     0.6041   3.078  0.00217 ** 
## c      24.2189     2.2757  10.643  < 2e-16 ***
## d       0.8635     0.1783   4.844 1.58e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.197 on 667 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (44 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91049, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8413, p-value = 0.0001224
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6765     2158.6                                
## 2   6741     2080.3 24 78.309  10.573 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model     AIC
## 1     1 25640.9
## 2     2 25357.7
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.05246    0.33762   6.079 1.27e-09 ***
## alpha  0.19626    0.03521   5.574 2.58e-08 ***
## a      0.28168    0.10946   2.573   0.0101 *  
## b      2.02187    0.14790  13.671  < 2e-16 ***
## c     58.28046    1.20100  48.527  < 2e-16 ***
## d      1.38453    0.07252  19.091  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5555 on 6741 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8308     4415.0                                
## 2   8253     4106.1 55 308.95   11.29 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40211.66
## 2     2 39423.66
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5859     0.2011   2.913  0.00359 ** 
## alpha   0.5816     0.0560  10.386  < 2e-16 ***
## a       1.3424     0.4624   2.903  0.00371 ** 
## b       2.7847     0.4599   6.055 1.47e-09 ***
## c      33.9072     1.3047  25.988  < 2e-16 ***
## d       1.5505     0.2059   7.529 5.65e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7054 on 8253 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (56 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    890     500.00                         
## 2    883     494.01  7 5.9895  1.5294 0.1536
##   model      AIC
## 1     1 3721.381
## 2     2 3697.880
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.4737     1.3321   1.857 0.063637 .  
## alpha   0.3960     0.1599   2.476 0.013465 *  
## a       1.5488     0.3126   4.954 8.71e-07 ***
## b       1.2686     0.3565   3.559 0.000393 ***
## c      29.6844     1.9960  14.872  < 2e-16 ***
## d       0.4998     0.1042   4.799 1.87e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.748 on 883 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94889, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1798, p-value = 0.001474
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1000     566.90                                
## 2    987     516.99 13 49.915  7.3303 7.303e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4308.841
## 2     2 4184.325
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.3797     1.7725   1.907   0.0569 .  
## alpha   0.4663     0.1130   4.126 4.00e-05 ***
## a       0.0000     4.4807   0.000   1.0000    
## b       1.8149     4.4748   0.406   0.6851    
## c      26.3622     4.6564   5.662 1.97e-08 ***
## d       2.6767     3.9677   0.675   0.5001    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7237 on 987 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94511, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.1117, p-value = 9.858e-10
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3140     2796.3                                
## 2   3127     2664.1 13 132.19  11.935 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17424.89
## 2     2 17231.79
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.62499    0.29743  -5.463 5.04e-08 ***
## alpha  0.94738    0.07600  12.466  < 2e-16 ***
## a      6.32427    0.60136  10.517  < 2e-16 ***
## b      5.07175    0.95536   5.309 1.18e-07 ***
## c     34.84127    1.54541  22.545  < 2e-16 ***
## d      0.31391    0.05278   5.948 3.02e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.923 on 3127 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (91 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92896, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -14.134, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1681     625.59                                
## 2   1668     611.40 13 14.183  2.9764 0.0002512 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8778.340
## 2     2 8695.476
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -2.32950    0.25968  -8.971  < 2e-16 ***
## alpha  0.55587    0.11127   4.996 6.48e-07 ***
## a      6.75834    0.67411  10.026  < 2e-16 ***
## b      7.53989    1.40145   5.380 8.50e-08 ***
## c     31.57505    0.96997  32.553  < 2e-16 ***
## d      0.19588    0.03937   4.975 7.21e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6054 on 1668 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (303 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89657, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8998, p-value = 9.628e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    360     160.54                         
## 2    359     159.48  1 1.0664  2.4005 0.1222
##   model      AIC
## 1     1 1023.403
## 2     2 1022.970
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.3791     0.3247  -7.326 1.58e-12 ***
## alpha   0.2538     0.1576   1.610 0.108204    
## a       0.0000     5.2542   0.000 1.000000    
## b       3.2741     5.3043   0.617 0.537455    
## c      58.2488    17.1354   3.399 0.000751 ***
## d       2.0200     2.3362   0.865 0.387822    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6665 on 359 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94694, p-value = 3.647e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.17226, p-value = 0.8632
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1736     1481.0                                
## 2   1719     1349.9 17 131.13  9.8227 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5173.137
## 2     2 5002.900
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.68338    0.62335  -1.096    0.273    
## alpha  0.48981    0.06448   7.597 4.96e-14 ***
## a      0.72851    0.17907   4.068 4.95e-05 ***
## b      1.17595    0.22440   5.240 1.80e-07 ***
## c     63.66139    4.20757  15.130  < 2e-16 ***
## d      1.13138    0.16134   7.012 3.36e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8862 on 1719 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (31 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85337, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6803, p-value = 2.864e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2527     1959.3                                
## 2   2485     1819.5 42 139.81  4.5466 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9211.166
## 2     2 9025.020
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.5737     0.5748  -0.998    0.318    
## alpha   0.6926     0.0598  11.582  < 2e-16 ***
## a       0.5800     0.1237   4.688 2.90e-06 ***
## b       1.8716     0.2791   6.706 2.47e-11 ***
## c      79.9119     4.7168  16.942  < 2e-16 ***
## d       1.4716     0.1221  12.048  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8557 on 2485 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (121 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87891, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.7054, p-value = 1.16e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 28 rows containing missing values (`geom_point()`).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1699     965.89                                
## 2   1670     879.44 29 86.456  5.6612 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7044.476
## 2     2 6860.189
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.19761    0.80332  -0.246    0.806    
## alpha  0.75046    0.06295  11.921  < 2e-16 ***
## a      0.81952    0.19093   4.292 1.87e-05 ***
## b      3.07569    0.58099   5.294 1.36e-07 ***
## c     52.55816    1.85863  28.278  < 2e-16 ***
## d      1.27999    0.08125  15.754  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7257 on 1670 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (77 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92247, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6369, p-value = 3.537e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Error in nls(fg1_MBg5, data = G_M334, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     1       NA
## 2     2 1309.945
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -3.4115     0.1414 -24.130  < 2e-16 ***
## alpha   0.7070     0.1736   4.073 5.74e-05 ***
## a       0.0000    46.3162   0.000  1.00000    
## b       3.8782    46.1586   0.084  0.93309    
## c      73.7708    27.1585   2.716  0.00693 ** 
## d       2.1008    14.6687   0.143  0.88620    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4355 on 349 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (104 observations deleted due to missingness)

summary

  • simple model: does not fit
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89926, p-value = 1.373e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.5551, p-value = 0.0003779
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) 2
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6877 2876 1.3848730 0.0748353 0.8486091 1.9211370 0.1811536 0.0015833 0.1031516 0.2591555 0.5263456 0.2026339 0.8500573 2.1840036 1.8100492 2.557958 52.12308 50.23617 54.00999 1.3162156 1.1484390 1.4839923
212 Laurentian Mixed Forest east 22715 9499 2.0436775 0.0615505 1.5573915 2.5299635 0.1840190 0.0007930 0.1288230 0.2392149 0.3375402 0.2961316 0.3789487 1.6722398 1.5541956 1.790284 41.35770 40.52962 42.18579 1.2321897 1.1889520 1.2754274
221 Eastern Broadleaf Forest east 7333 3571 -0.6047095 0.0201792 -0.8831755 -0.3262435 0.5472479 0.0017315 0.4656788 0.6288170 1.2408049 0.3535657 2.1280442 3.3410563 2.4387504 4.243362 46.44359 42.67601 50.21117 1.7544197 1.3539400 2.1548993
222 Midwest Broadleaf Forest east 5845 2589 0.2761072 0.0677959 -0.2343492 0.7865636 0.4064780 0.0026500 0.3055568 0.5073992 0.7552514 0.5364225 0.9740803 2.6161630 2.3021221 2.930204 52.52465 49.35936 55.68994 1.3433048 1.1981811 1.4884284
223 Central Interior Broadleaf Forest east 10010 3864 -0.4673159 0.0169623 -0.7226155 -0.2120163 0.3751687 0.0018806 0.2901611 0.4601764 1.2758492 0.6064927 1.9452056 2.5733896 1.9004829 3.246296 36.25752 33.92030 38.59474 1.4802421 1.1665894 1.7938948
231 Southeastern Mixed Forest east 13517 6193 2.2571276 0.0575847 1.7867555 2.7274998 0.6028199 0.0004948 0.5592179 0.6464220 0.6629863 0.4884947 0.8374779 3.4706941 3.1893379 3.752050 24.60260 23.94226 25.26294 1.5392390 1.4517707 1.6267073
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.8244973 0.0591150 1.3479164 2.3010781 0.5897383 0.0005176 0.5451419 0.6343347 0.5260296 0.3098075 0.7422517 3.3975908 3.0826554 3.712526 23.73576 22.98479 24.48674 1.6272648 1.5177596 1.7367699
234 Lower Mississippi Riverine Forest east 1388 778 1.6458810 1.0915390 -0.4037106 3.6954726 0.7133667 0.0083055 0.5345821 0.8921514 1.7279771 -1.3521265 4.8080806 2.1117320 -0.9925619 5.216026 26.02966 18.85758 33.20174 1.5413404 -0.2825841 3.3652649
242 Pacific Lowland Mixed Forest pacific 83 83 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2295 906 1.0604150 0.3067958 -0.0259339 2.1467640 0.0597909 0.0118427 -0.1536466 0.2732284 1.5719618 0.8830379 2.2608857 0.9551704 0.2804365 1.629904 40.21823 33.20688 47.22958 1.2289884 0.4864271 1.9715497
255 Prairie Parkland (Subtropical) east 717 319 1.5527641 3.2876685 -2.0074891 5.1130173 0.4144618 0.0361922 0.0409157 0.7880080 0.8691588 0.2681406 1.4701769 1.8594003 0.6731608 3.045640 24.21891 19.75060 28.68721 0.8634886 0.5134683 1.2135090
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 2.0524650 0.1139898 1.3906157 2.7143142 0.1962572 0.0012396 0.1272394 0.2652749 0.2816799 0.0670973 0.4962624 2.0218714 1.7319418 2.311801 58.28046 55.92613 60.63480 1.3845270 1.2423570 1.5266971
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 0.5858719 0.0404452 0.1916460 0.9800977 0.5815931 0.0031358 0.4718230 0.6913633 1.3423766 0.4359066 2.2488467 2.7846809 1.8831181 3.686244 33.90718 31.34955 36.46481 1.5504926 1.1468078 1.9541773
M223 Ozark Broadleaf Forest Meadow east 896 349 2.4737178 1.7744035 -0.1406699 5.0881054 0.3960003 0.0255750 0.0821289 0.7098717 1.5488194 0.9352237 2.1624150 1.2685974 0.5689455 1.968249 29.68435 25.76689 33.60181 0.4998401 0.2954160 0.7042642
M231 Ouachita Mixed Forest east 1006 495 3.3796722 3.1419235 -0.0987219 6.8580663 0.4663090 0.0127724 0.2445313 0.6880867 0.0000000 -8.7928005 8.7928005 1.8149034 -6.9663721 10.596179 26.36222 17.22465 35.49979 2.6767393 -5.1093776 10.4628563
M242 Cascade Mixed Forest pacific 3224 3207 -1.6249863 0.0884664 -2.2081701 -1.0418026 0.9473772 0.0057756 0.7983673 1.0963872 6.3242662 5.1451565 7.5033759 5.0717474 3.1985456 6.944949 34.84127 31.81115 37.87139 0.3139076 0.2104263 0.4173889
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -2.3295002 0.0674339 -2.8388339 -1.8201666 0.5558682 0.0123817 0.3376188 0.7741176 6.7583368 5.4361435 8.0805300 7.5398852 4.7911078 10.288663 31.57505 29.67257 33.47754 0.1958766 0.1186471 0.2731062
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.3791059 0.1054593 -3.0177473 -1.7404646 0.2537727 NA -0.0561435 0.5636888 0.0000000 -10.3328579 10.3328579 3.2741473 -7.1573053 13.705600 58.24883 24.55040 91.94726 2.0199533 -2.5744450 6.6143515
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 -0.6833826 0.3885644 -1.9059857 0.5392204 0.4898101 0.0041572 0.3633492 0.6162709 0.7285113 0.3772948 1.0797278 1.1759506 0.7358182 1.616083 63.66139 55.40890 71.91389 1.1313750 0.8149317 1.4478184
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.5737481 0.3303502 -1.7008079 0.5533117 0.6926439 0.0035765 0.5753726 0.8099151 0.5800462 0.3374351 0.8226573 1.8715548 1.3242808 2.418829 79.91191 70.66262 89.16119 1.4716127 1.2320888 1.7111367
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 -0.1976127 0.6453232 -1.7732331 1.3780077 0.7504567 0.0039630 0.6269827 0.8739307 0.8195240 0.4450315 1.1940165 3.0756917 1.9361484 4.215235 52.55816 48.91268 56.20364 1.2799943 1.1206378 1.4393509
M334 Black Hills Coniferous Forest interior west 459 181 -3.4114692 0.0199885 -3.6895343 -3.1334041 0.7070400 0.0301308 0.3656412 1.0484388 0.0000000 -91.0939058 91.0939058 3.8781713 -86.9058271 94.662170 73.77076 20.35576 127.18575 2.1007581 -26.7493369 30.9508530
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 15 rows containing missing values (`geom_point()`).

plot b coefficient

## Warning: Removed 15 rows containing missing values (`geom_point()`).

plot c coefficient

## Warning: Removed 1 rows containing missing values (`geom_hline()`).
## Warning: Removed 15 rows containing missing values (`geom_point()`).

plot d coefficient

## Warning: Removed 15 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (stand biomass productivity in % 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US   0.79308110             0.08157866   0.9529752745
## 2       pacific  -0.16263683             0.01835199  -0.1266669228
## 3          east   1.03388386             0.06860422   1.1683481326
## 4 interior west  -0.07816593             0.04014652   0.0005212438
##   95 % CI, lower
## 1      0.6331869
## 2     -0.1986067
## 3      0.8994196
## 4     -0.1568531

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.45776092              0.011261773     0.47983399
## 2       pacific     0.06979184              0.005454635     0.08048293
## 3          east     0.31562087              0.009064148     0.33338659
## 4 interior west     0.07234821              0.003862086     0.07991790
##   95 % CI, lower
## 1     0.43568785
## 2     0.05910076
## 3     0.29785514
## 4     0.06477852

Analaysis 2: \(G_{TI-NoIngrow}\)

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6869     3216.6                                
## 2   6817     3001.3 52 215.24  9.4015 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24882.32
## 2     2 24354.11
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.16043    0.28343   4.094 4.29e-05 ***
## alpha  0.83630    0.03869  21.616  < 2e-16 ***
## a      0.50001    0.04546  10.998  < 2e-16 ***
## b      1.83267    0.09803  18.695  < 2e-16 ***
## c     68.73905    1.24051  55.412  < 2e-16 ***
## d      0.97466    0.03780  25.782  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6635 on 6817 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (54 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  19351      23127                                 
## 2  18862      21107 489 2019.9  3.6913 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 63998.00
## 2     2 61697.03
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.66279    0.25717   6.466 1.03e-10 ***
## alpha  1.04253    0.02698  38.646  < 2e-16 ***
## a      0.27895    0.01349  20.673  < 2e-16 ***
## b      1.24888    0.04750  26.290  < 2e-16 ***
## c     60.91140    0.79454  76.663  < 2e-16 ***
## d      1.01774    0.01990  51.144  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.058 on 18862 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3847 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 40 rows containing missing values (`geom_point()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7319     3643.2                                
## 2   7255     3434.1 64 209.17  6.9047 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 31554.54
## 2     2 30990.74
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.65757    0.14783  -4.448 8.79e-06 ***
## alpha  0.84728    0.04206  20.145  < 2e-16 ***
## a      0.94746    0.18176   5.213 1.91e-07 ***
## b      3.02566    0.20483  14.772  < 2e-16 ***
## c     62.64769    2.62270  23.887  < 2e-16 ***
## d      1.49835    0.11404  13.139  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.688 on 7255 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (72 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   5044     4308.4                                 
## 2   4824     3738.3 220 570.14  3.3442 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19723.24
## 2     2 18609.23
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.30609    0.28763   1.064    0.287    
## alpha  0.99466    0.04942  20.127   <2e-16 ***
## a      0.58787    0.05500  10.689   <2e-16 ***
## b      2.24090    0.12610  17.772   <2e-16 ***
## c     63.29329    1.67388  37.812   <2e-16 ***
## d      1.06029    0.04909  21.601   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8803 on 4824 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1015 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 8 rows containing missing values (`geom_point()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   8872     6007.8                                 
## 2   8730     5691.6 142 316.19  3.4153 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 34828.86
## 2     2 34001.35
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.80380    0.12364  -6.501 8.42e-11 ***
## alpha  0.75737    0.04413  17.163  < 2e-16 ***
## a      0.85355    0.17271   4.942 7.87e-07 ***
## b      2.44175    0.18175  13.435  < 2e-16 ***
## c     50.68176    1.21271  41.792  < 2e-16 ***
## d      1.30262    0.09013  14.452  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8074 on 8730 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1274 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (`geom_point()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13446      12254                                 
## 2  13195      11035 251 1218.4  5.8042 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66367.52
## 2     2 64659.57
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.76047    0.25552    6.89 5.84e-12 ***
## alpha  0.94544    0.02543   37.18  < 2e-16 ***
## a      0.46747    0.03053   15.31  < 2e-16 ***
## b      3.08669    0.12281   25.13  < 2e-16 ***
## c     34.31153    0.51813   66.22  < 2e-16 ***
## d      1.27386    0.02659   47.91  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9145 on 13195 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (316 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (`geom_point()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13504      15331                                 
## 2  13221      13799 283 1531.5   5.185 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 65934.14
## 2     2 64083.77
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.38805    0.25226   5.502 3.81e-08 ***
## alpha  0.96451    0.02494  38.666  < 2e-16 ***
## a      0.39168    0.03382  11.580  < 2e-16 ***
## b      2.90579    0.12250  23.720  < 2e-16 ***
## c     32.75286    0.52980  61.821  < 2e-16 ***
## d      1.31061    0.02994  43.781  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.022 on 13221 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (402 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 57 rows containing missing values (`geom_point()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1368     2135.0                                
## 2   1316     1984.8 52 150.18  1.9149 0.0001261 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7497.623
## 2     2 7297.936
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5051     0.9766   0.517    0.605    
## alpha   0.9019     0.1202   7.500 1.17e-13 ***
## a       0.8976     0.2284   3.930 8.95e-05 ***
## b       2.8449     0.5751   4.947 8.51e-07 ***
## c      41.4473     3.4014  12.185  < 2e-16 ***
## d       1.1039     0.1655   6.670 3.76e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.228 on 1316 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84765, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5987, p-value = 4.252e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1888     1534.7                                 
## 2   1773     1348.7 115 185.99  2.1261 2.171e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6937.884
## 2     2 6459.937
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.0492     0.5646   1.858   0.0633 .  
## alpha   0.4953     0.1033   4.794 1.77e-06 ***
## a       0.7461     0.1645   4.537 6.10e-06 ***
## b       1.3449     0.2007   6.700 2.79e-11 ***
## c      55.2406     2.6391  20.931  < 2e-16 ***
## d       1.1183     0.1392   8.033 1.72e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8722 on 1773 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (516 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90528, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -10.817, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing missing values (`geom_point()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    710     3128.3                         
## 2    667     3030.4 43 97.922  0.5012  0.997
##   model      AIC
## 1     1 3570.774
## 2     2 3515.063
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    5.00000    7.01224   0.713   0.4761    
## alpha  0.61584    0.29378   2.096   0.0364 *  
## a      0.12245    0.09309   1.315   0.1888    
## b      1.09126    0.80152   1.361   0.1738    
## c     29.62861    2.55155  11.612  < 2e-16 ***
## d      0.88881    0.14392   6.176 1.14e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.132 on 667 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (44 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89301, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.9434, p-value = 7.678e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6765     3120.3                                
## 2   6741     2911.9 24 208.47  20.108 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23241.99
## 2     2 22770.74
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.56276    0.34187   4.571 4.94e-06 ***
## alpha  0.82601    0.03582  23.058  < 2e-16 ***
## a      0.26185    0.03568   7.339 2.40e-13 ***
## b      1.76955    0.10462  16.914  < 2e-16 ***
## c     74.40239    1.70488  43.641  < 2e-16 ***
## d      1.08187    0.03872  27.938  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6572 on 6741 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8308     4928.4                                
## 2   8253     4767.3 55 161.05   5.069 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 37694.53
## 2     2 37285.40
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.17350    0.26044   4.506 6.70e-06 ***
## alpha  0.90599    0.05733  15.804  < 2e-16 ***
## a      0.67282    0.16239   4.143 3.46e-05 ***
## b      2.34356    0.18881  12.412  < 2e-16 ***
## c     47.55653    1.19002  39.963  < 2e-16 ***
## d      1.37435    0.09108  15.090  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.76 on 8253 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (56 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    890     702.27                                
## 2    883     680.17  7 22.094  4.0975 0.0001935 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3537.006
## 2     2 3503.262
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     4.2321     2.3616   1.792  0.07347 .  
## alpha   1.0090     0.1732   5.827 7.92e-09 ***
## a       0.0000     0.2513   0.000  1.00000    
## b       1.3190     0.4329   3.047  0.00238 ** 
## c      42.4816     2.7686  15.344  < 2e-16 ***
## d       1.2773     0.2536   5.036 5.77e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8777 on 883 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96657, p-value = 2.1e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1895, p-value = 0.001425
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

##   model      AIC
## 1     1 4182.168
## 2     2 4126.965
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     5.0000     3.2307   1.548   0.1220    
## alpha   0.8349     0.1325   6.302 4.43e-10 ***
## a       0.0000     0.2800   0.000   1.0000    
## b       1.1840     0.4826   2.453   0.0143 *  
## c      45.8648     5.6255   8.153 1.07e-15 ***
## d       1.7341     0.4164   4.165 3.39e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9318 on 987 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93432, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.534, p-value = 6.404e-11
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3140     2906.2                                
## 2   3127     2742.5 13 163.73   14.36 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16154.59
## 2     2 15943.37
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -1.62004    0.29143  -5.559 2.94e-08 ***
## alpha  1.07370    0.07235  14.840  < 2e-16 ***
## a      0.00000    2.04174   0.000  1.00000    
## b      6.03100    2.07752   2.903  0.00372 ** 
## c     95.71565    6.88773  13.897  < 2e-16 ***
## d      2.47175    0.59045   4.186 2.91e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9365 on 3127 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (91 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90935, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.763, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 17 rows containing missing values (`geom_point()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1681     1785.5                                
## 2   1668     1729.8 13 55.706  4.1321 8.879e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7935.257
## 2     2 7839.811
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.2749     0.2530  -8.993  < 2e-16 ***
## alpha   0.8288     0.1093   7.585 5.50e-14 ***
## a       3.6697     0.8554   4.290 1.89e-05 ***
## b       3.3994     0.8311   4.090 4.51e-05 ***
## c      41.8919     8.2424   5.082 4.14e-07 ***
## d       1.3979     0.4362   3.205  0.00138 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.018 on 1668 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (303 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9102, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1525, p-value = 0.001619
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 10 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    360     195.96                                
## 2    359     188.52  1 7.4343  14.157 0.0001964 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 988.1197
## 2     2 976.0028
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.6700     0.2688  -9.932  < 2e-16 ***
## alpha   0.6216     0.1517   4.097 5.18e-05 ***
## a       0.0000     2.0273   0.000   1.0000    
## b       3.3517     2.0895   1.604   0.1096    
## c      70.7341    13.5838   5.207 3.24e-07 ***
## d       1.6872     0.9213   1.831   0.0679 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7247 on 359 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93536, p-value = 1.71e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1936, p-value = 0.2326
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1736     1676.4                                
## 2   1719     1561.1 17 115.28   7.467 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4364.968
## 2     2 4242.489
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.33750    1.03019   0.328    0.743    
## alpha  0.74430    0.06142  12.117  < 2e-16 ***
## a      0.47885    0.11135   4.300 1.80e-05 ***
## b      0.71388    0.15703   4.546 5.85e-06 ***
## c     81.01354    4.97015  16.300  < 2e-16 ***
## d      0.89656    0.10601   8.458  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.953 on 1719 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (31 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87825, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.6786, p-value = 1.358e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 11 rows containing missing values (`geom_point()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2527     2344.7                                
## 2   2485     2116.1 42 228.58  6.3913 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8552.063
## 2     2 8324.449
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.65832    0.55077  -1.195    0.232    
## alpha  0.95413    0.05599  17.041  < 2e-16 ***
## a      0.45198    0.07716   5.858 5.32e-09 ***
## b      1.90207    0.26351   7.218 6.97e-13 ***
## c     89.95195    4.04062  22.262  < 2e-16 ***
## d      1.25137    0.07441  16.817  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9228 on 2485 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (121 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86245, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.7053, p-value = 2.535e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 22 rows containing missing values (`geom_point()`).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1699     1220.6                                
## 2   1670     1059.2 29 161.46  8.7783 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6534.582
## 2     2 6295.314
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.90446    1.28317   0.705    0.481    
## alpha  0.97795    0.06105  16.019  < 2e-16 ***
## a      0.45844    0.11249   4.075 4.81e-05 ***
## b      2.33387    0.54745   4.263 2.13e-05 ***
## c     63.93883    1.88255  33.964  < 2e-16 ***
## d      1.08203    0.04659  23.225  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7964 on 1670 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (77 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91344, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.206, p-value = 5.434e-10
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing missing values (`geom_point()`).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    357     618.39                            
## 2    349     584.57  8 33.819  2.5238 0.01114 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1072.454
## 2     2 1042.319
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.1952     0.9020  -1.325    0.186    
## alpha   0.6866     0.1670   4.110 4.93e-05 ***
## a       0.0000     7.8286   0.000    1.000    
## b       1.4054     7.8112   0.180    0.857    
## c     125.1995   121.6202   1.029    0.304    
## d       2.5030     9.5252   0.263    0.793    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.294 on 349 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (104 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96219, p-value = 6.081e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.952, p-value = 7.749e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) 2
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6877 2876 1.1604259 0.0803348 0.6048069 1.7160449 0.8362965 0.0014969 0.7604536 0.9121393 0.5000053 0.4108841 0.5891266 1.8326695 1.6405045 2.024834 68.73905 66.30725 71.17085 0.9746629 0.9005549 1.048771
212 Laurentian Mixed Forest east 22715 9499 1.6627923 0.0661342 1.1587245 2.1668601 1.0425348 0.0007277 0.9896582 1.0954114 0.2789529 0.2525040 0.3054017 1.2488840 1.1557702 1.341998 60.91140 59.35403 62.46877 1.0177355 0.9787307 1.056740
221 Eastern Broadleaf Forest east 7333 3571 -0.6575707 0.0218534 -0.9473585 -0.3677829 0.8472846 0.0017689 0.7648373 0.9297318 0.9474617 0.5911585 1.3037649 3.0256591 2.6241391 3.427179 62.64769 57.50643 67.78896 1.4983497 1.2748002 1.721899
222 Midwest Broadleaf Forest east 5845 2589 0.3060902 0.0827332 -0.2578033 0.8699837 0.9946592 0.0024422 0.8977762 1.0915421 0.5878730 0.4800546 0.6956914 2.2408996 1.9936958 2.488103 63.29329 60.01172 66.57487 1.0602947 0.9640641 1.156525
223 Central Interior Broadleaf Forest east 10010 3864 -0.8037979 0.0152878 -1.0461690 -0.5614269 0.7573657 0.0019472 0.6708652 0.8438662 0.8535535 0.5150103 1.1920968 2.4417477 2.0854721 2.798023 50.68176 48.30456 53.05895 1.3026216 1.1259365 1.479307
231 Southeastern Mixed Forest east 13517 6193 1.7604710 0.0652897 1.2596180 2.2613239 0.9454435 0.0006466 0.8956020 0.9952850 0.4674666 0.4076299 0.5273034 3.0866903 2.8459632 3.327418 34.31153 33.29592 35.32713 1.2738604 1.2217378 1.325983
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.3880549 0.0636354 0.8935880 1.8825218 0.9645061 0.0006222 0.9156109 1.0134013 0.3916840 0.3253825 0.4579854 2.9057852 2.6656656 3.145905 32.75286 31.71437 33.79135 1.3106095 1.2519320 1.369287
234 Lower Mississippi Riverine Forest east 1388 778 0.5050705 0.9537550 -1.4107998 2.4209409 0.9019106 0.0144595 0.6660129 1.1378083 0.8975931 0.4494886 1.3456977 2.8448715 1.7167162 3.973027 41.44734 34.77454 48.12015 1.1039359 0.7792314 1.428640
242 Pacific Lowland Mixed Forest pacific 83 83 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2295 906 1.0492351 0.3187643 -0.0581012 2.1565713 0.4953403 0.0106756 0.2926932 0.6979874 0.7461268 0.4235561 1.0686975 1.3449033 0.9512167 1.738590 55.24059 50.06447 60.41671 1.1183398 0.8452875 1.391392
255 Prairie Parkland (Subtropical) east 717 319 5.0000000 49.1714701 -8.7687168 18.7687168 0.6158412 0.0863059 0.0389990 1.1926834 0.1224478 -0.0603301 0.3052256 1.0912636 -0.4825347 2.665062 29.62861 24.61857 34.63866 0.8888098 0.6062183 1.171401
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 1.5627630 0.1168750 0.8925900 2.2329360 0.8260140 0.0012833 0.7557899 0.8962380 0.2618459 0.1919077 0.3317841 1.7695542 1.5644627 1.974646 74.40239 71.06028 77.74450 1.0818700 1.0059582 1.157782
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 1.1734964 0.0678271 0.6629757 1.6840171 0.9059890 0.0032864 0.7936131 1.0183650 0.6728182 0.3544915 0.9911450 2.3435560 1.9734481 2.713664 47.55653 45.22380 49.88927 1.3743461 1.1958080 1.552884
M223 Ozark Broadleaf Forest Meadow east 896 349 4.2321282 5.5772489 -0.4029152 8.8671716 1.0089725 0.0299867 0.6691064 1.3488385 0.0000000 -0.4931357 0.4931357 1.3190460 0.4694354 2.168657 42.48165 37.04789 47.91541 1.2773301 0.7795053 1.775155
M231 Ouachita Mixed Forest east 1006 495 5.0000000 10.4375433 -1.3398667 11.3398667 0.8348546 0.0175510 0.5748792 1.0948300 0.0000000 -0.5495270 0.5495270 1.1840165 0.2369666 2.131066 45.86482 34.82547 56.90416 1.7340675 0.9169601 2.551175
M242 Cascade Mixed Forest pacific 3224 3207 -1.6200395 0.0849295 -2.1914466 -1.0486325 1.0737045 0.0052348 0.9318430 1.2155661 0.0000000 -4.0032924 4.0032924 6.0310044 1.9575578 10.104451 95.71565 82.21073 109.22058 2.4717520 1.3140355 3.629469
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -2.2748631 0.0639943 -2.7710372 -1.7786890 0.8287531 0.0119390 0.6144409 1.0430652 3.6696912 1.9919430 5.3474395 3.3993748 1.7693322 5.029417 41.89193 25.72538 58.05847 1.3978848 0.5422963 2.253473
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.6699792 0.0722686 -3.1986552 -2.1413033 0.6216039 0.0230193 0.3232302 0.9199776 0.0000000 -3.9868125 3.9868125 3.3516574 -0.7574843 7.460799 70.73407 44.02026 97.44787 1.6872174 -0.1245214 3.498956
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 0.3375011 1.0612959 -1.6830611 2.3580633 0.7443000 0.0037730 0.6238247 0.8647754 0.4788522 0.2604549 0.6972496 0.7138755 0.4058792 1.021872 81.01354 71.26537 90.76171 0.8965640 0.6886500 1.104478
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.6583167 0.3033530 -1.7383417 0.4217083 0.9541320 0.0031350 0.8443378 1.0639262 0.4519820 0.3006746 0.6032894 1.9020737 1.3853496 2.418798 89.95195 82.02862 97.87527 1.2513715 1.1054579 1.397285
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 0.9044642 1.6465338 -1.6123334 3.4212618 0.9779452 0.0037271 0.8582027 1.0976877 0.4584394 0.2378010 0.6790778 2.3338740 1.2601154 3.407633 63.93883 60.24642 67.63123 1.0820320 0.9906527 1.173411
M334 Black Hills Coniferous Forest interior west 459 181 -1.1951917 0.8135475 -2.9691698 0.5787863 0.6866001 0.0279025 0.3580674 1.0151329 0.0000000 -15.3972638 15.3972638 1.4053772 -13.9576020 16.768356 125.19953 -114.00112 364.40018 2.5029949 -16.2309912 21.236981
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 15 rows containing missing values (`geom_point()`).

plot b coefficient

## Warning: Removed 15 rows containing missing values (`geom_point()`).

plot c coefficient

## Warning: Removed 1 rows containing missing values (`geom_hline()`).
## Warning: Removed 19 rows containing missing values (`geom_point()`).

plot d coefficient

## Warning: Removed 15 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US   0.70060747             0.10293723     0.90236445
## 2       pacific  -0.16065851             0.01796126    -0.12545444
## 3          east   0.87405707             0.08477051     1.04020727
## 4 interior west  -0.01279109             0.05556463     0.09611559
##   95 % CI, lower
## 1      0.4988505
## 2     -0.1958626
## 3      0.7079069
## 4     -0.1216978

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US      0.8962475              0.011356331      0.9185059
## 2       pacific      0.0852987              0.005259694      0.0956077
## 3          east      0.7100316              0.009324231      0.7283071
## 4 interior west      0.1009172              0.003789538      0.1083446
##   95 % CI, lower
## 1     0.87398906
## 2     0.07498970
## 3     0.69175612
## 4     0.09348966